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dc.contributor.authorVan Vleck, Erik S.
dc.contributor.authorMallet-Paret, John
dc.contributor.authorCahn, John W.
dc.date.accessioned2015-04-02T16:10:26Z
dc.date.available2015-04-02T16:10:26Z
dc.date.issued1999-03-05
dc.identifier.citationVan Vleck, Erik., Mallet-Paret, John., Cahn, John W. "Traveling Wave Solutions for Systems of ODEs on a Two-Dimensional Spatial Lattice." (1999) SIAM J. Appl. Math., 59(2), 455–493. (39 pages). http://dx.doi.org/10.1137/S0036139996312703.en_US
dc.identifier.urihttp://hdl.handle.net/1808/17284
dc.descriptionThis is the published version, also available here: http://dx.doi.org/10.1137/S0036139996312703.en_US
dc.description.abstractWe consider infinite systems of ODEs on the two-dimensional integer lattice, given by a bistable scalar ODE at each point, with a nearest neighbor coupling between lattice points. For a class of ideal nonlinearities, we obtain traveling wave solutions in each direction $e^{i\theta}$, and we explore the relation between the wave speed c, the angle $\theta$, and the detuning parameter a of the nonlinearity. Of particular interest is the phenomenon of "propagation failure," and we study how the critical value $a=a^*(\theta)$ depends on $\theta$, where $a^*(\theta)$ is defined as the value of the parameter a at which propagation failure (that is, wave speed c=0) occurs. We show that $a^*:\Bbb{R}\to\Bbb{R} is continuous at each point $\theta$ where $\tan\theta$ is irrational, and is discontinuous where $\tan\theta$ is rational or infinite.en_US
dc.publisherSociety for Industrial and Applied Mathematicsen_US
dc.subjecttraveling wavesen_US
dc.subjectpropagation failureen_US
dc.subjectanisotropyen_US
dc.subjectAllen--Cahn equationen_US
dc.titleTraveling Wave Solutions for Systems of ODEs on a Two-Dimensional Spatial Latticeen_US
dc.typeArticle
kusw.kuauthorVan Vleck, Erik
kusw.kudepartmentMathematicsen_US
dc.identifier.doi10.1137/S0036139996312703
kusw.oaversionScholarly/refereed, publisher version
kusw.oapolicyThis item does not meet KU Open Access policy criteria.
dc.rights.accessrightsopenAccess


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